Oh most definitely. He's the first human (besides Gothel) that she's ever properly met so she probably doesn't even know what she's feeling.

^ *agrees 100%*

I think it was Flynn Rider that started to fall for Rapunzel because he was flirting with her when he was doing that smoulder and she was looking at him as if to say ewh im not interested in you and when they were trapped in the dam Flynn told Rapunzel that his real name was Eugene Fitzherbert and he was an orphan. But it was when they were on the boat that you kinda realise what is going to happen as he was about to kiss her and he didn’t plus the dude sacrificed his own life for her. (if you seen the film you know what scene im talking about).

Flynn Rider: I don’t know not who you are nor how I came to find you but may I just say Hey how are you doing the name’s Flynn Rider so how is your day so far hmm.

LOL

I think he's completely in love with her from the beginning... I would picked both, but Rapunzel falls for him, for me, in the campfire scene... That "I think he likes me...!" maybe means she really hopes he has feelings for her too... I don't know... xD
I agree with all who picked Flynn

Yeah I agree it has to be Flynn, cause when Rapunzel first step out the dark into the light and Flynn first saw he was like in a trance or say daze "Uh hah" was exact words.And he was the first one to reaveal a secsert about himself to which he probley never ever revealed to anybody before Rapunzel.And after all he was the first one to almost kiss her! He probbley would've if he was distracted from the brothers shining thier latern from the shoreline to distract him from Rapunzel.And of course he risked his own life to save her in the tower around the ending.